Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅1018

  title={Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅1018},
  author={Tom{\'a}s Oliveira e Silva and Siegfried Herzog and Silvio Pardi},
  journal={Math. Comput.},
This paper describes how the even Goldbach conjecture was confirmed to be true for all even numbers not larger than 4 · 1018. Using a result of Ramaré and Saouter, it follows that the odd Goldbach conjecture is true up to 8.37 · 1026. The empirical data collected during this extensive verification effort, namely, counts and first occurrences of so-called minimal Goldbach partitions with a given smallest prime and of gaps between consecutive primes with a given even gap, are used to test several… Expand
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